Proper Orthogonal Decomposition and Model Reduction of Nonlinear Systems

This work deals with the application of the proper orthogonal decomposition (POD) to structural dynamics. On one hand, a physical interpretation of the proper orthogonal modes (POM) is given using the singular value decomposition (SVD). It is shown that the POM converge to the normal modes under some circumstances. On the other hand, the POM are exploited for model reduction purposes. The efficiency of the reduced model for the prediction of the response is tested on a nonlinear beam. The comparison with another reduced model obtained via the normal modes of the linearised system points out that the POM are optimal for the reconstruction of the dynamics of a system.